Processing monopole headwaves for compressional and shear slowness values is a well-established service for Logging While Drilling (“LWD”) sonic logging and wireline sonic logging. Propagation speed of monopole headwaves is essentially constant over a wide frequency band. On the other hand, propagation speed of borehole modes such as leaky-p, borehole flexural and borehole quadrupole modes change as a function of frequency. These modes are therefore known as dispersive modes. It is well-known that dispersion curves contain information about physical properties of formations surrounding the borehole.
Slowness-Frequency Analysis (“SFA”) is widely used as a visual quality-control (“QC”) for post-processing of the recorded LWD sonic logging data or well-site processing for wireline sonic logging data. According to conventional SFA techniques, the dispersions are first extracted/calculated from the measured waveforms using a modified matrix pencil algorithm, for example, which is described in detail in Ekstrom, M. P., Dispersion Estimation From Borehole Acoustic Arrays Using a Modified Matrix Pencil Algorithm: 29th Asilomar Conference on Signals, Systems, and Computers (1995). Then, the dispersions are projected onto the slowness axis. These techniques are well-known in the art. For example, conventional SFA techniques are described in U.S. Pat. No. 7,643,374, entitled “SLOWNESS-FREQUENCY PROJECTION DISPLAY AND ANIMATION.” It should be understood that conventional SFA techniques are computationally expensive, requiring a large number of operations to extract the dispersions.